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If the system of equations x + 2y − 3z = 2 2x + λy + 5z = 5 14x + 3y + μz = 33 has infinitely many solutions, then λ + μ is equal to :
- 13
- 10
- 11
- 12
Correct answer: 12
Solution
For the system to have infinitely many solutions, the equations must be dependent, which typically occurs when the coefficients of the variables in the equations are proportional. By applying the conditions for dependency, we find that λ must equal 10 and μ must equal 2, leading to λ + μ = 12.
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